What is the variation in total cost on account of variation in the proportion in which the labour/labor types are engaged?
This information is provided by the labour/labor mix or Gang Composition variance.

The problem data arranged in a working table:

Standard [Production: 7,500 units]

Actual [Production: 7,125 units]

Time(hrs)

Rate(Rs/hr)

Cost(Rs)

Rate(Rs/hr)

Gross/Total

Net

Abnromal

Time(hrs)

Cost(Rs)

Time(hrs)

Cost(Rs)

Time(hrs)

Cost(Rs)

Skilled

200

20

4,000

22

240

5,280

216

4,752

24

528

Semi Skilled

400

15

6,000

14

500

7,000

450

6,300

50

700

Un Skilled

150

10

1,500

12

220

2,640

198

2,376

22

264

Total

750

11,500

960

14,920

864

13,428

96

1,492

The Formulae » Labor/Labour Mix/Gang-Composition Variance (LMV/GCV)

That part of the variance in the total cost of labour/labor on account of a variation between the standard mix (standard proportion in which labour/labor time of various labour/labor types are to be employed) and the proportion of actual mix (proportion in which they are actually used). It is a part of the Labour/Labor Usage/Efficiency Variance or a Sub-Part of the Labour/Labor Cost Variance.

When two or more types of labour/labor are used for the manufacture of a product, the total Labour/Labor Mix/Gang-Composition Variance is the sum of the variances measured for each labour/labor type separately.

⇒ TLMV/TGCV

=

LMV/GCVSk + LMV/GCVSe + ....

Direct Formula

There is no direct formula for calculating the total mix variance

LMV/GCV » Formula interpretation

The above formulae for Labour/Labor Mix/Gang-Composition Variance, can be used in all cases i.e. both when ATMix = STMix as well as when ATMix ≠ STMix. When ATMix ≠ STMix, the ratio ATMix/STMix works as a correction factor to readjust the ST to ST for AI and thereby the SC to SC for AI.

Actual Time ⇒ Net Time

Wherever you find the presence of actual time in the formula, you should interpret it as Actual (Net) Time. Where there abnormal loss of time, the actual time is segregated into two as abnormal loss time and net time. Even in such cases, for the purpose of calculating the Mix/Gang-Composition Variance, the (Net) time should be considered for actual time.

Where ATMix = STMix

ATMix/STMix becomes 1 thus nullifying its effect, in which case the formula would read as:

For each labour/labor type separately

LMV/GCV

=

(ST × SR) − (AT × SR)

=

(ST − AT) × SR

Caution:

The formula for Labour/Labor Efficiency/Usage Variance also reads the same [LEV/LUV = (ST × SR) − (AT × SR)] when AO = SO.
In case of Mix Variance the condition to be satisfied is ATMix = STMix.

LMV/GCV = 0

Labour/Labor mix or Gang Composition variance for each labour/labor type would be zero, when the proportion of the actual time of labour/labor types to the total time of actual mix (AT/AT(AM)) is the same as the proportion of the standard time of the labour/labor types to the total time of standard mix (ST/ST(SM)).

LMV/GCV for each labour/labor type would be zero, when the proportion of the labour/labor time of each labour/labor type to the time of mix is the

same both in the standards as well as actuals. i.e. when

STLab

STMix

=

AT(N)Lab

ATMix

Where there is only one labour/labor type being used, there is no meaning in thinking of the Labour/Labor Mix/Gang-Composition Variance.
Where LMV/GCV = 0, the total efficiency/usage variance is nothing but Yield Variance.

LEV/LUV

=

LMV/GCV + LYV/LSUV/LSEV

=

0 + LYV/LSUV/LSEV

=

LYV/LSUV/LSEV

TLMV/TGCV = 0

When more than one type of labour/labor is used, the total LMV/GCV may become zero

when the LMV/GCV on account of each labour/labor type is zero, or

when the proportion of labour/labor times inter-se between them both as per the standard and the actual is the same. ST1 : ST2 : ... = AT(N)1 : AT(N)2 : ...

when the unfavourable variance due to one or more labour/labor types is set off by the favourable variance due to one or more other labour/labor types.

Therefore, it would not be appropriate to conclude that there is no variance on account of any labour/labor type just because the total LMV/GCV is zero.

Solution [Using the data as it is]

For working out problems with the data considered as it has been given without having to do any recalculations, use the above formulae (which are capable of being used in all cases)

Consider the working table above:

Standard [Production: 7,500 units]

Actual [Production: 7,125 units]

Time(hrs)

Rate(Rs/hr)

Cost(Rs)

Rate(Rs/hr)

Total

Normal

Abnromal

Time(hrs)

Cost(Rs)

Time(hrs)

Cost(Rs)

Time(hrs)

Cost(Rs)

Skilled

200

20

4,000

22

240

5,280

216

4,752

24

528

Semi Skilled

400

15

6,000

14

500

7,000

450

6,300

50

700

Un Skilled

150

10

1,500

12

220

2,640

198

2,376

22

264

Total

750

11,500

960

14,920

864

13,428

96

1,492

Using,

LMV/GCV

=

({

AT(N)Mix

STMix

× STLab} − AT(N)Lab) × SRLab

Labour/Labor Mix or Gang Composition Variance due to labourers/laborers who are

• Skilled

=

({

864 hrs

750 hrs

× 200 hrs} − 216 hrs) × Rs. 20/hr

=

({1.152 × 200 hrs) − 216 hrs) × Rs. 20/hr

=

(230.4 hrs − 216 hrs) × Rs. 20/hr

=

(+ 14.4 hrs) × Rs. 20/hr

=

+ Rs. 288

⇒ LMV/GCVSk

=

+ Rs. 288

[Fav]

• Semi-skilled

=

({

864 hrs

750 hrs

× 400 hrs} − 450 hrs) × Rs. 15/hr

=

({1.152 × 400 hrs) − 450 hrs) × Rs. 15/hr

=

(460.8 hrs − 450 hrs) × Rs. 15/hr

=

(+ 10.8 hrs) × Rs. 15/hr

=

+ Rs. 162

⇒ LMV/GCVSe

=

+ Rs. 162

[Fav]

• Unskilled

=

({

864 hrs

750 hrs

× 150 hrs} − 198 hrs) × Rs. 10/hr

=

({1.152 × 150 hrs) − 198 hrs) × Rs. 10/hr

=

(172.8 hrs − 198 hrs) × Rs. 10/hr

=

(− 25.2 hrs) × Rs. 10/hr

=

− Rs. 252

⇒ LMV/GCVUn

=

− Rs. 252

[Adv]

Total Labour Mix/Gang-Composition Variance

+ Rs. 198

[Fav]

Solution [Using recalculated data]

Where you find that the STMix ≠ AT(N)Mix, you may alternatively recalculate the standard to make the STMix = AT(N)Mix and use the figures relating to the recalculated standard in the working table. In such a case, the formulae that you use would look simpler (without the adjustment factor AT(N)Mix/STMix).

From the data relating to the problem, it is evident that STMix ≠ AT(N)Mix. Thus we recalculate the standard data for Actual Input [Refer to the calculations].

Consider the recalculated standard data and the actual data arranged in a working table.

Standard [Production: 8,640 units]

Actual [Production: 7,125 units]

Time(hrs)

Rate(Rs/hr)

Cost(Rs)

Rate(Rs/hr)

Total

Normal

Abnromal

Time(hrs)

Cost(Rs)

Time(hrs)

Cost(Rs)

Time(hrs)

Cost(Rs)

Skilled

230.4

20

4,608

22

240

5,280

216

4,752

24

528

Semi Skilled

460.8

15

6,912

14

500

7,000

450

6,300

50

700

Un Skilled

172.80

10

1,728

12

220

2,640

198

2,376

22

264

Total

864

13,248

960

14,920

864

13,428

96

1,492

Using LMV/GCV = (ST − AT) SR [Since AT(AM) = ST(SM)]

Labour/Labor Mix or Gang Composition Variance due to labour/labor type which are

Skilled

=

(230.4 hrs − 216 hrs) × Rs. 20/hr

=

(+ 14.4 hrs) × Rs. 20/hr

=

+ Rs. 288

⇒ LMV/GCVSk

=

+ Rs. 288

[Fav]

Semi-skilled

=

(460.8 hrs − 450 hrs) × Rs. 15/hr

=

(+ 10.8 hrs) × Rs. 15/hr

=

− Rs. 162

⇒ LMV/GCVSe

=

− Rs. 162

[Adv]

Unskilled

=

(172.8 hrs − 198 hrs) × Rs. 10/hr

=

(− 25.2 hrs) × Rs. 10/hr

=

− Rs. 252

⇒ LMV/GCVUn

=

− Rs. 252

[Adv]

Total Labour Mix/Gang-Composition Variance

+ Rs. 198

[Fav]

Note:

This formula can be used only when AT(N)Mix = STMix

You don't need to recalculate the standard

The formula with the adjustment factor AT(N)Mix/STMix can be used in all cases i.e. both when AT(N)Mix = STMix and AT(N)Mix ≠ STMix. Therefore, you don't need to rebuild the working table by recalculating the standards for the purpose of finding the variances.

These formulae can be used both for each labour/labor type separately as well as for all the labour/labor types together

LEV/LUVN = LMV/GCV + LYV/LSUV ⇒ (1)

For each Labour/Labor Type Separately

LMV/GCVLab = LEV/LUV(N)Lab − LYV/LSUVLab

For All Labour/Labor Types Together

TLMV/TGCV = TLEV/TLUVN − TLYV/TLSUV

LCV = LRPV + LMV/GCV + LYV/LSUVN + LITV ⇒ (2)

For each Labour/Labor Type Separately

LMV/GCVLab = LCVLab − LRPVLab − LYV/LSUV(N)Lab − LITVLab

For All Labour/Labor Types Together

TLMV/TGCV = TMCV − TMPV − TLYV/LSUV(N) − TLITV

Who is held responsible for the Variance?

Since this variance is on account of the variation in the ratio in which the constituent labour/labor types are mixed i.e. the gang composition being different from the standard ratio, the people or department responsible for authorising the work time usage and mixing of component labourers/laborers for production can be held responsible for this variance.